Spectrum resources for wireless communications are very limited and most of them have been already assigned to licensed users. However, it turns out that spectrum bands are sparsely utilized temporally and spatially.
A cognitive radio aims at improving the spectral efficiency by allowing a secondary user to opportunistically utilize such spectrum resources.
Thus, spectrum sensing to check if the spectrum band of interest is occupied becomes one of the most important tasks of a secondary user to avoid the interference to a primary user.
Interference in wireless channels are usually modeled by a wide-sense stationary (WSS) random process. However, an information-bearing signal is often better modeled by a widesense cyclostationary (WSCS) random process, of which properties have been intensively investigated in communications and signal processing.
The second-order cyclostationarity (SOCS) is defined by the periodicity of the mean, the autocovariance, and the complementary auto-covariance functions with a common period. In particular, if the complementary auto-covariance function does not vanish, the SOCS random process becomes an improper-complex SOCS process.
Such an improper-complex SOCS random signal is observed when the primary user transmits an improper-complex second-order stationary data sequence using a linear modulation scheme such as pulse amplitude modulation (PAM), quadrature amplitude modulation (QAM), single sideband (SSB), vestigial sideband (VSB), and minimum shift keying (MSK) modulations. It is noteworthy that the second-order cyclostationarity combined with the impropriety exhibits periodic and symmetric spectral correlation.
A number of presence detection techniques have been developed to perform spectrum sensing for cognitive radios.
These are roughly classified as a matched filter detector, an energy detector, a cyclostationary feature detector, and their variants. Although the matched filter detector offers a better detection performance, it requires the perfect knowledge on the primary-user signal and its timing. The energy detector has the simplest structure. However, it suffers from poor performance and high sensitivity to the uncertainty in the noise variance.
To the contrary, the cyclostationary feature detector exploits only the second-order statistical properties of the primary-user signal but shows better robustness to the uncertainty in the noise variance.